Chemical Physics 542 (2021) 111055

Available online 26 November 20200301-0104/© 2020 Elsevier B.V. All rights reserved.

Structural, electronic, and adsorbed properties of Be-rich nanoalloys: BenPt (n = 1–10) clusters

Qiman Liu a,b,*, Yunhu Hu a, Xiaoyan Zhang a, Fengwu Wang a, Longjiu Cheng c,*

a School of Chemical and Materials Engineering, Huainan Normal University, Huainan 232038, PR China b Anhui Province Key Laboratory of Low Temperature Co-fired Materials, Huainan, 232038, PR China c Department of Chemistry, Anhui Province Key Laboratory of Chemistry for Inorganic/Organic Hybrid Functionalized Materials, Anhui University, Hefei, 230601, PR China

A R T I C L E I N F O

Keywords: Hume-Rothery phases Alloy clusters Structural evolution Superatoms σ-Hole

A B S T R A C T

The Hume-Rothery alloy phases of the main-group elements are rather rare, of which the phase stability mechanisms are decided by the electronic effects. The intermetallic compound Be-Pt alloy is a member of this family, but structural and electronic characters of them at nanometer scale still remain unclear. In this work, the geometric structures, stabilities and electronic properties of BenPt clusters (n = 1–10) are first investigated using the method combining the genetic algorithm with density function theory (DFT). Benchmark calculations indicate that the PBE-D3 functional is reliable in predicting the energetic sequences of four isomers of Be4Pt cluster compared to the high-level coupled cluster method. In general, the most structures of the alloy clusters can be obtained by replacing one beryllium atom in the pure beryllium (Bem, m = 2–11) clusters with a Pt atom. We found that the Be4Pt and Be10Pt clusters are two very stable 8e/20e superatoms in this series, respectively, where the electronic structure of Pt atom is d10. Analyses of electrostatic potential surfaces show that these two clusters have significant σ-holes with most positive potential regions, which can be seen as binding sites with Lewis bases. When a CO molecule is adsorbed on the superatom clusters, the C––O stretching frequency has a large red-shift and the bond length is slightly elongated, due to the electrons of the clusters transfer to the anti- bond π orbital of CO. This work gives inferences for further understanding structural characters of the binary alloy from the nanoscale view.

1. Introduction

Intermetallic compounds have great structural diversity, in which the majority of alloy phases adopt crystal structures with different numbers of metal atoms per unit cell [1–3]. In comparison with atomic radius, the electronic effects have a prominent influence on the structure stability of those compounds [4,5]. The remarkable relationship be-tween structures and electron counts in these so-called electron-phases has been illuminated by a variety of insights. The Be-Pt alloy is a member of this family [6], which have been the subjects of intense study because the Hume-Rothery phases of the main-group elements are rather rare. Generally, beryllium-rich alloys show interesting structural features with high coordination numbers as in the structure of Be17Ru3 compound [7]. However, the structural characterization of Be-rich compounds remains challenging because of the low X-ray scattering power of the beryllium atoms. Therefore, there are some early reports

about the Pt-Be systems that refer to Be-rich compounds with large unit cells, but no further structural investigations were performed [8].

Recently, the crystal structure and physicochemical properties of the γ-phase Be21Pt5 as well as the analysis of the concomitant chemical bonding are reported [9]. The structure of this alloy can be understood as comprising of polyhedral clusters where the relative arrangement of these cluster units determines the observed translational periodicity. In fact, many alloys with Cu5Zn8-type (γ-brass) structures, often called γ-phases, are also treated as an assembly of nested polyhedral clusters [10]. For example, Cu9Al4, Ag5Zn8 and Cu9In4 are all typical γ-brass alloys [11,12]. It is generally believed that the structural description of solid solutions is complicated. As is well known, the clusters represent initial forms of condensed matter, and build a bridge from micro to macro in spatial scale. Hence, the study of alloy clusters is helpful to understand structural characters and some properties of bulk materials from the microscopic level. However, to our knowledge there has been

* Corresponding authors at: School of Chemical and Materials Engineering, Huainan Normal University, Huainan 232038, PR China (C. Liu). E-mail addresses: qimliu@ustc.edu.cn (Q. Liu), clj@ustc.edu.cn (L. Cheng).

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Chemical Physics

journal homepage: www.elsevier.com/locate/chemphys

https://doi.org/10.1016/j.chemphys.2020.111055 Received 29 August 2020; Received in revised form 16 November 2020; Accepted 18 November 2020

Chemical Physics 542 (2021) 111055

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no theoretical study of sub-nanometer Be-Pt alloys. For a stable metal cluster, it is usually described using a jellium

model [13,14], which assumes a uniform background of positive charge of the cluster’s atomic nuclei and the innermost electrons, in which valence electrons move freely and are affected by the external potential. Therefore, the entire cluster can be regarded as a superatom [15–17], and the energy levels of electrons are arranged as 1S21P61D102S21F142P6 and so on, associated with magic numbers 2, 8, 18, 34, 40 etc. The superatom model has been successfully used in explaining the stability of metal clusters with closed-shell electronic structure [18,19]. The well-known example of Al13, with 39 valence electrons, needs one extra electron to close the 2P6 shells and behaves as a halogen atom [20].

Metal clusters exhibit excellent catalytic performance and are known as the fourth generation of the catalyst, which are widely used in carbon monoxide (CO) catalytic oxidation reaction, fuel cell reaction, water gas conversion reaction, and nitrogen oxide (NOx) catalytic decomposition reaction in the field of chemical industry [21–23]. For example, Pt clusters are standard catalysts for the oxygen reduction reaction ORR, which is the principal reaction in PEMFCs [24–26]. Rodríguez-Kessler calculated the adsorption of O and OH on Pt12-13 clusters and found that the oxygen adsorption on the 3-fold hollow sites increases for the clus-ters with the highest coordination number [27]. Munoz-Castro et al. reported that the Pt6Ag6 cluster has a closed shell geometric structure and may serve as a potential catalytic candidate for hydrogenation re-actions [25]. Moreover, the usage of single atom dopants has been investigated in the context of catalysis, which is a very effective strategy to reduce the amount of precious metal [28–31]. Cao and co-workers explored Pd-doped Cu clusters and found that a single Pd atom at the edge site of the Cu55 cluster can considerably reduce the activation en-ergy of H2 dissociation [32].

In contrast to the well-developed understanding of beryllium clusters [33–38], there is relatively less information available about structural and electronic properties of bimetallic Be-Pt systems. In fact, metal atoms doped Be clusters have been reported, involving the structures and properties of the BenMg [39], BenLi [40] and TM-Ben (TM = Fe, Co, Ni) [41], etc. Here we perform an unbiased global search of geometric structures of BenPt (n = 1–10) and Bem (m = 2–11) clusters using genetic algorithm (GA) combined directly with DFT method, and try to under-stand structural characters of Be-Pt alloys from the nanoscale view. The structures, stabilities, and electronic properties of the alloy clusters are reported in detail. Moreover, we explain the adsorbed behaviors that have been obtained from the clusters upon the CO adsorption.

2. Computational details

The low-lying and global minimum structures of BenPt (n = 2–10) and Bem (m = 2–11) clusters are located by unbiased global search of the GA-DFT method, which is successfully used to structural predictions of many metal clusters [42–44]. GA is a search heuristic that mimics the process of natural selection. This heuristic is routinely used to generate useful solutions to optimization and search problems. GA belongs to the larger class of evolutionary algorithms, which generate solutions to optimization problems using techniques inspired by natural evolution, such as inheritance, mutation, selection, and crossover. In this work, more than 1000 samplings are optimized by DFT at each constituent. In the global research of the potential energy surfaces of the studied clus-ters, a small basis set (Def2-SVP) is adopted for saving time. After global optimization, the low-lying isomers are fully relaxed at the PBE-D3/ Def2-TZVP level of theory [45,46], and the frequencies are also calcu-lated at this level to ensure that they are true local minimums. For en-ergetic parameters, zero-point energy corrections are also included. All calculations are accomplished by the GAUSSIAN 09 package [47].

To verify the reliability of the DFT methods used in this work, a benchmark calculation is performed by comparing relative stability of four low-energy isomers of Be4Pt cluster calculated in different methods.

Table 1 gives the results of the benchmark calculation for DFT/Def2- TZVP and CCSD(T)/Def2-QZVP. It can be seen that, gaps of the rela-tive energies for the four Be4Pt isomers optimized in the PBE-D3 func-tional are consistent with those in CCSD(T) method. Moreover, the calculated bond length of the Be2 dimer in the PBE-D3 functional is 2.49 Å, which is also in good agreement with the experimental value (2.45 Å) [48].

Energies for 4-1I are in atomic units, while other energies are relative to this in eV.

3. Results and discussion

The low-energy isomers of BenPt (n = 1–10) and Bem (m = 2–11) clusters are fully relaxed at the PBE-D3/Def2-TZVP level of theory. The spin multiplicities (S) are set to 1, 3, 5, and 7 to find the most stable isomers. It is worth noting that there are too many isomers for each cluster, and only showing some low-lying isomers within 2 eV of the global minimum. The isomers are verified to be true local minimums on the potential energy surfaces by frequency check. Bare beryllium clus-ters have been explored in literatures [34,49], and all the structures are reproduced in this work.

3.1. Geometries

The lowest-energy structures together with some low-lying isomers of BenPt (n = 1–10) and corresponding bare Bem (m = 2–11) clusters are shown in Fig. 1. The global minima (GM) of BePt is a linear configura-tion with singlet state, where the distance between Be and Pt atoms is 1.91 Å. Three isomers of Be2Pt are triangle structures with C2v symme-try. Among them, the GM is a triplet state. A triangular pyramid with C3v symmetry is the most stable structure for Be3Pt, which is also a triplet state. The GM of Be4Pt has a C3v structure with singlet state, which can be obtained by replacing one beryllium atom in the bi-pyramid Be5 with a Pt atom. The second isomer of the cluster in which the Pt atom lies at the vertex of the quadrilateral pyramid is 0.34 eV higher in energy. The Be6 is a high-symmetry Oh octahedron with the sevent state, while the GM of Be5Pt has a hat motif with Cs symmetry. The structure of Be6Pt is in C3v symmetry and based on octahedron, which is a triplet state. The structures of Be8 and Be7Pt clusters are also based on the octahedron. Similar to the configuration of the ground-state Be9 cluster, Be8Pt is a tricapped trigonal prism. The GM of Be9Pt is in Cs symmetry. Four iso-mers of Be10Pt are all singlet states, in which the GM is a spherical cage with Cs symmetry.

Overall, compared to pure Be clusters, there is substantial recon-struction after doped a Pt atom. Generally speaking, the 2D → 3D transition of the beryllium-rich alloy clusters is found to occur in Be3Pt, and the structural transition from the compact to hollow-cage structure is found at n = 8. Moreover, the Pt atom is not often endohedrally doped during the growth, but gradually moves from convex to surface sites, trending to settle in sites with lower-coordination numbers.

Table 1 Comparison of single point energies for the four low-lying isomers of Be4Pt.

Method 4-1I 4-1II 4-1III 4-1IIII

CCSD(T) − 177.814211 0.24 1.52 1.56 TPSSH − 178.307766 0.42 1.59 2.02 TPSS − 178.335958 0.37 1.60 2.01 TPSS-D3 − 178.338866 0.42 1.59 1.89 PBE0 − 178.200597 0.47 1.64 2.02 PBE0-D3 − 178.252832 0.37 1.69 1.94 B3LYP − 178.365858 0.43 1.29 1.66 B3LYP-D3 − 178.370097 0.50 1.28 1.49 M062x − 178.186043 0.55 1.62 2.09 BPW91 − 178.437917 0.33 1.61 1.93 PBE − 178.250950 0.34 1.70 2.02 PBE-D3 − 178.258215 0.34 1.72 1.89

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3.2. Binding energies and stability

It is well known that the relative stability of the different sized clusters can be discussed on the basis of the binding energy per atom (Eb), the adsorption energy (Ead) and the second difference in energy (Δ2E), which are defined as the following formulas:

Eb = [nE(Be) + E(Pt)-E(BenPt)]/(n + 1); Ead = E(Ben-1Pt) + E(Be) - E(BenPt); Δ2E = E(Ben+1Pt) + E(Ben-1Pt)-2E(BenPt),where E represents the

energy of the corresponding atom or cluster. Plots of these quantities as a function of the number n of Be atoms in

the BenPt clusters are shown in Fig. 2. As shown in Fig. 2a, the Eb curve of the alloy clusters increase nearly monotonically when n grows.

However, it is clear that the Eb curve has a local maxima at n = 4. From the definition of the Eb equation, we can say that the Be4Pt cluster possesses relatively higher stability than its respective neighbors. This finding is in agreement with the fact that the Be4 is a quite stable pure Be cluster. The reason may be that these two clusters are all electronic shell closure. Fig. 2b shows the Ead values of BenPt (n = 1–10) clusters. Up to n = 6, the adsorption energy curve presents a typical odd–even pattern, and the distinct peak appears at n = 4. From the Δ2E curve in the Fig. 2c, we infer that the BenPt clusters exhibit an odd–even oscillation behavior, but distinct peak also occurs at n = 4. It is also evidenced that the Be4Pt cluster is salient on the binding energy curve. These results clearly show that the Be4Pt is a very stable magic cluster. Moreover, here it is important to mention that the relatively stability of Be10Pt cluster

Fig 1. Optimized structures and relative stability of BenPt (n = 1–10) at PBE-D3/Def2-TZVP level. Labeled are symmetry, energy (eV) relative to the GM one and spin multiplicities.

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cannot be directly compared according to the definition of these two curves. Furthermore, we also give the numerical values of binding en-ergies (Erel = nE(Be) + E(Pt)-E(BenPt)) and HOMO-LUMO gaps of the clusters in Table S1 of the supplementary material.

3.3. Electronic structure

The quest for chemically inert (stable) cluster species is a leading thread in current research. In general, the stability of lead clusters is determined by the interplay between geometrical and electronic struc-tural features. When electron shells are closed, this result in size- dependent stability feature. The HOMO-LUMO gap of the Be4Pt cluster is 1.44 eV at the PBE/Def2-TZVP, suggesting a very favorable magic electronic structure. In order to shed some light on the origins of high stability of the cluster, we further investigated its molecular orbitals. The 2 s2 electrons of beryllium atom and 5d96s1 electrons of Pt atom are valence electrons respectively. As shown in Fig. 3a, the HOMO, HOMO-1 and HOMO-8 orbitals are typical super 1Pz, 1Py and 1S orbitals from

their shapes, respectively. Moreover, we can also see that the 5d-type lone pairs are completely localized in Pt atom from these three or-bitals. The HOMO-2 and HOMO-3 orbitals are only 5d-type lone pairs of Pt atom. Hence, the electron filled shells of the superatomic Be4Pt cluster is 1S21P6 where the contribution comes from the 2 s2 electrons of Be atoms, and the electronic structure of Pt atom is indeed d10. The d10

electronic structure of Pt atom has been reported in the icosahedral PtPb12

2- alloy cluster [50], where the Pb and Pt atoms donate two elec-trons and zero electrons to cluster bonding, respectively.

It is clear that the 5d10 electrons of Pt atom as lone pairs are completely localized in the Be4Pt superatom. According to the electron counting rule, the Be10Pt cluster has 20 valence electrons, also satisfying the magic number in Jellium model. Fig. 3b show the molecular orbitals (MOs) of the Be10Pt cluster. The HOMO orbital has one 2S character, and the next five MOs exhibit dominant 1D characters, then followed by three 1P and one 1S orbitals. Moreover, the cluster also has a large HOMO-LUMO gap (1.07 eV). Thus, the electronic shell of the Be10Pt superatom is 1S21P61D102S2. Furthermore, the lowest-energy structure

Fig 2. (a) The binding energies per atom (Eb), (b) the adsorption energy (Ead) and (c) the second-order differences of energies (Δ2E) for BenPt (n = 1–10) clusters.

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of Be8Pt cluster is a spherical cage with C2v symmetry, which is a triplet state and has 18-valence electron. From the MO orbitals in the Fig. S1, the Be8Pt cluster is a magnetic superatom with [1S21P61D8]1D12S1

electronic shell.

3.4. CO adsorption

The CO molecule adsorbed by alloy nanostructures has attracted increasing attention [51–54], due to it being involved in several energy- related and environmental processes.

The stable Be4Pt and Be10Pt clusters have closed electronic and geometric shells. However, there is a very large number of possibility sites for the CO adsorption on the clusters so that some basic rules for locating adsorption sites are indispensable. The molecular electrostatic potential V(r) is a well-established tool for analyzing chemical bonding and inter-molecular interactions [55], which is a physical observable that can be computed from an experimental or theoretical electron density distribution. As we know, the V(r) value of one atom is every-where positive, but it decreases monotonically toward zero when moving away from the nucleus. The formation of a molecule will result in a redistribution of the electron density toward the more electroneg-ative atoms and generation of regions of negative. Fig. 4a shows the electrostatic potential surface of the Be4Pt superatom, and there is a significant σ-hole with a positive potential region where it is a region of depleted electron density. Due to the doping of Pt atom, the valence 2 s- overlap between Be atoms is polarized in the Be4Pt cluster when forming the delocalized superatomic orbitals, and consequently V(r) is negative nearly over the cluster and most positive over a tiny area. The situation

in larger Be10Pt cluster is also similar, as shown in Fig. 4b. CO is a Lewis base, and its negative lone-pair regions are favor

attracted to the σ-hole sites with highest positive potential. It was pre-viously shown that the V(r) on the C atom of CO is more negative than that of the O atom. Hence, the C head tends to adsorb in the clusters more than the O head. Fig. 5 shows the adsorption structure for the CO molecule onto the Be4Pt. Although there may be several other local minimas, focus was placed on the most important minima wherein the CO base approaches the σ-hole. The distance of Be-C is 1.66 Å, which is

1P6

1S2

HOMO

HOMO-1 HOMO-2 HOMO-3

HOMO-4

HOMO-14

1P6

1S2

2S2

1D10

HOMO-12 HOMO-13HOMO-11

HOMO-7

Be10Pt, EHL=1.07 eV

HOMO

HOMO-1

HOMO-4

HOMO-8

Be4Pt, EHL=1.44 eV

(a) (b)

Fig 3. Structures and the molecular orbital diagrams of the (a) Be4Pt and (b) Be10Pt clusters.

Fig 4. Electrostatic potential surfaces of (a) Be4Pt and (b) Be10Pt clusters. Positive surfaces (σ-holes) are depicted in blue, and negative in green.

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in the range of Be-C bonds (1.66–1.73 Å) [56]. The C––O bond distance of 1.15 Å is slightly elongated due to the electron transfer to the anti- bond π orbital, as shown in the HOMO orbital of Be4Pt-CO. Moreover, we found that the interaction energy between CO and Be4Pt is 2.10 eV. The major interaction is σ-donation from the CO 5σ orbital to the metal cluster. In this complex the CO stretching frequency (2012.16 cm− 1) is < free CO (2208 cm− 1) [57]. It also points out that electron density is transferred from the cluster to the π-accepting orbital of the CO mole-cule, which explains the observed large red-shift in C––O stretching frequency. Other molecules (e.g. NO, N2 and O2) are adsorbed on the sigma-hole site of the Be4Pt superatom, and the bond lengths of them are also slightly elongated (Fig S2).

4. Conclusions

In summary, we first investigated the structural, electronic, and adsorbed properties of BenPt clusters in the size range (n = 1–10) using the GA-DFT method. Benchmark calculations indicate that the PBE-D3 functional is reliable in predicting the energetic sequences of four iso-mers of Be4Pt cluster compared to the high-level coupled cluster method. It is found that the most structures of the alloy clusters can be obtained by replacing one beryllium atom in the pure beryllium (Bem, m = 2–11) clusters with a Pt atom. The Eb, Δ2E and MOs results demon-strate that the Be4Pt and Be10Pt clusters are two very stable (1S21P6)/ (1S21P61D102S2) superatoms in this series, respectively. The contribu-tion of their superatom orbitals comes from the 2 s2 electrons of Be atoms, and the electronic structure of Pt atom is d10 in these two clusters. Analyses of electrostatic potential surfaces show that these two clusters have significant σ-holes with most positive potential regions. The re-gions as binding sites can interact with Lewis bases. After a CO molecule is adsorbed on the Be4Pt superatom, the C––O stretching frequency has a large red-shift and the bond length is slightly elongated. From the HOMO orbital shape of the Be4Pt-CO, it is clear that the electrons of the Be4Pt superatom transfer to the anti-bond π orbital of CO molecule.

CRediT authorship contribution statement

Qiman Liu: Methodology, Software, Writing - original draft. Yunhu Hu: . Xiaoyan Zhang: . Fengwu Wang: Writing - review & editing. Longjiu Cheng: Supervision.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work is financed by the National Natural Science Foundation of China (21873001). The calculations were carried out at the High- Performance Computing Center of Anhui University.

Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi. org/10.1016/j.chemphys.2020.111055.

References

[1] R.F. Berger, P.L. Walters, S. Lee, R. Hoffmann, Chem. Rev. 111 (2011) 4522. [2] L. Vitos, I.A. Abrikosov, B. Johansson, Phys. Rev. Lett. 87 (2001), 156401. [3] P.E.A. Turchi, M. Sluiter, F.J. Pinski, D.D. Johnson, D.M. Nicholson, G.M. Stocks, J.

B. Staunton, Phys. Rev. Lett. 67 (1991) 1779. [4] W. Hume-Rothery, Indian J. Phys. 11 (1969) 74. [5] T.B. Massalski, U. Mizutani, Prog. Mater. Sci. 22 (1978) 151. [6] A. Amon, A. Ormeci, M. Bobnar, L.G. Akselrud, M. Avdeev, R. Gumeniuk,

U. Burkhardt, Y. Prots, C. Hennig, A. Leithe-Jasper, Acc. Chem. Res. 51 (2018) 214. [7] D. Sands, Q.C. Johnson, O. Krikorian, K. Kromholtz, Acta Crystallogr. 15 (1962)

1191. [8] L. Misch, Metalltech. 15 (1936) 163. [9] A. Amon, E. Svanidze, A. Ormeci, M. Konig, D. Kasinathan, D. Takegami, Y. Prots,

Y.F. Liao, K.D. Tsuei, L.H. Tjeng, Angew. Chem. Int. Ed. 58 (2019) 15928. [10] O. Gourdon, D. Gout, D.J. Williams, T. Proffen, S. Hobbs, G.J. Miller, Inorg. Chem.

46 (2007) 251. [11] S. Westman, Acta Chem. Scand 22 (1968). [12] R. Marsh, Acta Crystallogr. 7 (1954) 379. [13] W. Knight, K. Clemenger, W.A. de Heer, W.A. Saunders, M. Chou, M.L. Cohen,

Phys. Rev. Lett. 52 (1984) 2141. [14] S. Khanna, P. Jena, Phys. Rev. Lett. 69 (1992) 1664. [15] Z. Luo, A.W. Castleman, Acc. Chem. Res. 47 (2014) 2931. [16] P. Jena, J. Phys. Chem. Lett. 4 (2013) 1432. [17] V. Chauhan, A.C. Reber, S.N. Khanna, Nat. Commun. 9 (2018) 1. [18] H. Hakkinen, Chem. Soc. Rev. 37 (2008) 1847. [19] X. Zhang, Y. Wang, H. Wang, A. Lim, G. Gantefoer, K.H. Bowen, J.U. Reveles, S.

N. Khanna, J. Am. Chem. Soc. 135 (2013) 4856. [20] D.E. Bergeron, A.W. Castleman, T. Morisato, S.N. Khanna, Science 304 (2004) 84.

2012.16 cm-1

785.8

628.6

471.5

314.3

157.2

0.0

IR in

tens

ities

(km

mol

-1)

Wavenumber (cm-1)0.0 600 1200 1800 2400

HOMO

Fig 5. The structure and infrared spectra (IR) of the Be4Pt-CO cluster.

Q. Liu et al.

Chemical Physics 542 (2021) 111055

7

[21] P. Rodríguez-Kessler, A. Rodríguez-Domínguez, J. Phys. Chem. C 119 (2015) 12378.

[22] S. Tian, Q. Fu, W. Chen, Q. Feng, Z. Chen, J. Zhang, W.-C. Cheong, R. Yu, L. Gu, J. Dong, Nat. Commun. 9 (2018) 1.

[23] P. Rodríguez-Kessler, P. Navarro-Santos, A. Rodríguez-Domínguez, Chem. Phys. Lett. 715 (2019) 141.

[24] T. Imaoka, H. Kitazawa, W.-J. Chun, S. Omura, K. Albrecht, K. Yamamoto, J. Am. Chem. Soc. 135 (2013) 13089.

[25] P. Rodríguez-Kessler, A. Munoz-Castro, P. Alonso-Davila, F. Aguilera-Granja, A. Rodríguez-Domínguez, J. Alloys Compd. 845 (2020), 155897.

[26] J.K. Nørskov, J. Rossmeisl, A. Logadottir, L. Lindqvist, J.R. Kitchin, T. Bligaard, H. Jonsson, J. Phys. Chem. B 108 (2004) 17886.

[27] P.L. Rodríguez-Kessler, A.R. Rodríguez-Domínguez, J. Chem. Phys. 143 (2015), 184312.

[28] P. Rodriguez-Kessler, S. Pan, E. Florez, J.L. Cabellos, G. Merino, J. Phys. Chem. C 121 (2017) 19420.

[29] P.L. Rodríguez-Kessler, P. Alonso-Davila, P. Navarro-Santos, J.A. Morato-Marquez, F. Ortíz-Chi, A.R. Rodríguez-Domínguez, J. Phys. Chem. C 123 (2019) 15834.

[30] P. Rodríguez-Kessler, A. Rodríguez-Domínguez, J. Morato-Marquez, F. Ortiz-Chi, D.M. Carey, A. Munoz-Castro, Chem. Phys. Lett. 754 (2020), 137721.

[31] J. Morato-Marquez, S. Godavarthi, C.G. Espinoza-Gonzalez, J.G. Torres-Torres, A. Rodríguez-Domínguez, A. Munoz-Castro, F. Ortiz-Chi, P. Rodríguez-Kessler, Chem. Phys. Lett. (2020), 137677.

[32] X. Cao, Q. Fu, Y. Luo, Phys. Chem. Chem. Phys. 16 (2014) 8367. [33] S. Khanna, F. Reuse, J. Buttet, Phys. Rev. Lett. 61 (1988) 535. [34] S. Srinivas, J. Jellinek, J. Chem. Phys. 121 (2004) 7243. [35] M.M. Marino, W.C. Ermler, J. Chem. Phys. 86 (1987) 6283. [36] M.K. Beyer, L.A. Kaledin, A.L. Kaledin, M.C. Heaven, V.E. Bondybey, Chem. Phys.

262 (2000) 15.

[37] A.M. Kolchin, R.W. Hall, J. Chem. Phys. 113 (2000) 4083. [38] J. Wang, G. Wang, J. Zhao, J. Phys. Conden. Matter 13 (2001) L753. [39] G.-X. Ge, Y.-L. Yan, F.-Z. Ren, X.-L. Lei, Z. Yang, W.-J. Zhao, Q.-L. Wang, Y.-H. Luo,

Chin. J. Chem. Phys. 20 (2007) 518. [40] X.-L. Lei, W.-J. Zhao, G.-X. Ge, Z. Yang, Y.-L. Yan, Y.-H. Luo, Phys. B: Condens.

Matter 403 (2008) 653. [41] G.-X. Ge, Y.-H. Luo, J.-W. Zhang, Acta Phys. Sin. 24 (2008) 1891. [42] Z. Tian, L. Cheng, Phys. Chem. Chem. Phys. 17 (2015) 13421. [43] W. Liu, L. Cheng, J. Phys. Chem. C 120 (2016) 2432. [44] A.N. Alexandrova, A.I. Boldyrev, Y.-J. Fu, X. Yang, X.-B. Wang, L.-S. Wang,

J. Chem. Phys. 121 (2004) 5709. [45] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [46] F. Weigend, R. Ahlrichs, Phys. Chem. Chem. Phys. 7 (2005) 3297. [47] G.W.T. M. J. Frisch, H. B. Schlegel, G. E. Scuseria,, G.S. M. A. Robb, V. Barone and

D. J. Fox, G. Revision B.01, Inc, Wallingford CT, 2009. [48] V. Bondybey, Chem. Phys. Lett. 109 (1984) 436. [49] V. Cerowski, B. Rao, S. Khanna, P. Jena, S. Ishii, K. Ohno, Y. Kawazoe, J. Chem.

Phys. 123 (2005), 074329. [50] E.N. Esenturk, J. Fettinger, Y.F. Lam, B. Eichhorn, Angew. Chem. Int. Ed. 43 (2004)

2132. [51] W.T. Wallace, R.L. Whetten, J. Am. Chem. Soc. 124 (2002) 7499. [52] Y. Gao, N. Shao, Y. Pei, X.C. Zeng, Nano Lett. 10 (2010) 1055. [53] J. Zhao, Q. Du, S. Zhou, V. Kumar, Chem. Rev. 120 (2020) 9021. [54] S. Zhou, W. Pei, Q. Du, J. Zhao, Phys. Chem. Chem. Phys. 21 (2019) 10587. [55] J.H. Stenlid, T. Brinck, J. Am. Chem. Soc. 139 (2017) 11012. [56] K. Nijesh, S. De, P. Parameswaran, Dalton Trans. 45 (2016) 7836. [57] X. Wu, L. Zhao, J. Jin, S. Pan, W. Li, X. Jin, G. Wang, M. Zhou, G. Frenking, Science

361 (2018) 912.

Q. Liu et al.